The Daily Mail says an exit strategy for him leaving this summer is in place.
The fear for Arsenal is that another season outside the Champions League will affect their ability to attract lucrative commercial deals.
They are negotiating a new kit deal which is due to start in the summer of 2019, with their Puma contract worth £30m a year expiring at the end of next season.
But any deal will hinge on reaching the Champions League.
Puma's rivals Nike and Adidas have shown an apprehension in investing huge money due to the uncertainty over when the club will be back in the Champions League.